Jolly Pirates can be tons of fun. For a more private setting, the joy of sailing, and a generally great day on the water, check out Tranquilo with Captain Anthony. Or, for great fun and a land-based excursion there is Aruba Bob. Here's a video interview with Kent and plenty of underwater footage showing the great stuff at Mangel Alto.
As much as I love Tranquilo, it is too long of a day for a 3 year old and your child in all likelihood would be bored.
Jolly Pirates would probably be okay for a boat ride, and the "pirate experience",
but the waters where they snorkel, more so from the perspective of a 3 yo, is pretty deep. Even their shallow snorkels are deep enough that an adult cannot stand.
The day we were on board it was not a "drunk fest". On board there was a large family group celebrating an upcoming wedding on the island and the rest of us were a mix of families and couples.
Have you considered renting gear and snorkeling from shore?
As much as we love Jolly Pirates, I wouldn't think of it as a Pirate experience that I child would expect. I think you would be disappointment. The crew don't really dress as pirates other than a jacket and maybe a hat sometimes. We have been twice, both times the crew was fun and flirty and we had a mix of families and couples, but the youngest were probabaly in the 10-12 year old range.
We just did the sunset snorkel trip on the Black Pearl yesterday. It leaves the pier at Moomba/Marriott Surf Club at 3:30 and gets back just after sunset. There are 2 snorkel stops along the coast at Boca Catalina and Malmok. They do not go to the Antilla as it has been leaking oil. It is a quiet trip, not a drunk fest, but has an open bar. Albert and Joann and first mate Anton make a wonderful crew. Joann remembers and calls everyone by name and makes wonderful sandwiches after the last dive. There are only 20 people on board total and there was 1 younger boy maybe 4 years old on our trip. The captain and first mate dove down and got starfish for him and others to look at and take pictures with. A great trip for those looking for a relaxing afternoon on the water. I highly recommend.